4 Quadratics and polynomials

Lesson

We have looked at a number of ways to solve quadratic equations . These include:

Factorising the quadratic expression and then using the null factor law. In particular, when the quadratic expression is non-monic, we can use techniques for non-monic quadratic trinomials.

Completing the square and then taking the square root of both sides of the equation.

Using the quadratic formula .

Solve 5x^{2}+22x+8=0 for x by factorising or otherwise.

Worked Solution

Solve 4x^{2}+11x+7=0 for x by completing the square or otherwise.

Worked Solution

Solve 4x^{2}+7x+3=0 for x by using the quadratic formula or otherwise.

Worked Solution

Idea summary

Ways to solve quadratic equations:

Factorising the quadratic expression and then using the null factor law.

Completing the square.

Using the quadratic formula.

Factorise monic and non-monic quadratic expressions and solve a wide range of quadratic equations derived from a variety of contexts.